Measurement of asymmetries. in e e production

Transcription

1 Measurement o asymmetries + + in e e production Daniele Trocino INFN and University o Torino 16th February 009 Particle Physics Ph.D. course (Pro. R. Demina)

2 Outline Introduction quick review o QED/EW couplings and cross sections the asymmetry and the importance o its measurement The experimental point o view the irst evidence measurements at the Z peak: observables at LEP I / SLC Examples o measurements: SLC vs LEP analysis strategies experimental problems: statistical and systematic errors some results

3 Fermion couplings to and Z i e e e c c g A 5 V i cos W ial Vectorial Ax Let Right where c V I 3 sin W Q or equivalently c R sin W Q ca I3 c L I 3 sin W Q L Q I3 ca cv 0 1/ el 1 1/ 1/ 1/ + sin W ul /3 1/ 1/ 4/3 sin W dl 1/3 1/ 1/ + /3 sin W er 1 0 sin W ur /3 0 4/3 sin W dr 1/3 0 /3 sin W and cv c L cr c A cl cr 3

4 e +e + cross sections 3 d e+ e + d cos s e 1 cos + d e+ e Z + 16 s d cos e V e A V 1 θ 4 A e+ { [ c c ][ c c ] 1 cos e e 8 cv c A cv c A cos with Pure exchange Pure Z exchange ~ 1 cos s GF M Z s 8 s M Z i s Z / M Z symmetric in cos contribute to total ~ 1 cos ~ cos asymmetry! 4 }

5 e +e + complete x section d + + e e d cos s 1 cos Z intererence 4 ℜ { s } cev c V 1 cos cea c A cos s 8 s s [ e V e A V A ] { [ c c ][ c c ] 1 cos 8 c Z e V c ea c V c A cos (1 + cos ) terms contribute to total cross section (e +e + ) cos terms only contribute to asymmetry in d d (e +e + ) due to (s), or s << MZ the cross section is dominated by while or s ~ MZ (near the Z peak) is dominated by Z moving away rom the Z peak, intererence contribution is signiicant both or cross section and or asymmetry 5 }

6 Asymmetries Forward events: [0, /] Backward events: [ /, ] Assuming that the process is mediated by a Z boson, we have asymmetries between orward and backward events because o the V A coupling o ermions to the Z (basically, ermions / anti ermions are more likely to be let handed / right handed) Initial state e e+ Final state cl Forward Z Backward e e+ cr Forward Z Backward cl cr cr cl 6

7 Fermion asymmetries Recalling the relation A cv c L cr, we deine the ermion asymmetries: c A cl cr L R cl c R c c cv c A V c c A c V /c A 1 cv /c A and write the dierential cross section or Z exchange as: d e+ e Z + 16 s [ cve c ea ][ c V c A ] 1 cos Ae A cos d cos NF ( F) is the number (cross section) o orward events NB ( B) is the number (cross section) o backward events Forward Backward asymmetry: 1 A FB NF N B NF N B F B F B ee d d cos d cos 0 1 ee d d cos d cos 0 0 ee d d cos d cos 1 0 ee d d cos d cos 1 3 A A 4 e 7

8 Forward Backward asymmetry ee FB A 3 Ae A 4 d Z 8 1 cos AFB cos d cos 3 only next to the Z peak! O peak: AeeFB Ae A s strongly depends on the C.M. energy! L.O. it to experimental data (QED corrections) 8

9 The importance o asymmetries (I) Essential test o the Standard Model o Electroweak Interactions proo o the V A structure o the weak interactions measurement o the Weinberg angle ( sin W ) A Sensitivity o A and AFB to sin W e,, u, c, t d, s, b ca 1 4 Q sin W A / (sin e) AFB AFB / (sin e) ~8 ~4 ~ ~ 1.8 ~ 4.4 ~ 5.7 b A ℓ, A FB give best estimates o sin W sensitivity to higher order electroweak corrections (e.g. LEP) A sin W cv sin e radiative corrections constraints on other ree parameter o the SM (Higgs mass, top mass) 9

10 The importance o asymmetries (II) Possible evidence o New Physics A values o Z peak give inormation about the Z intererence (predictible in the SM) or, possibly, intererences with other BSM neutral bosons ( Z'? ) ee cc, bb, tt are expected to provide evidence and perhaps measurements o possible new gauge interactions. Although b b inal states are quite easy to tag and can give evidence o such 0 0 new orces, but the B B mixing can make the quantitive measurements diicult c c, t t inal states suer less rom the mixing, but the c is more diicult to tag, while the t high mass makes the eect o such new interactions less signiicant 10

11 First evidence o asymmetry in e+e The irst evidence o asymmetry was ound in angular distribution o muons rom e+e collisions at PETRA in the 80's (C. M. energy ~ 34 GeV ) At these energies still dominates, asymmetry eects arise rom the Z tail LEP I, SLC will ocus on the Z peak to make precision measurements 11

12 Experiments at the Z peak with unpolarized beams When perorming an experiment with unpolarized e+/e beams with s ~ MZ one can measure AFB or all the (detectable and identiiable) outgoing ermions (e.g. LEP I case) ee FB A F B 3 Ae A TOT 4 in general, A cannot be determined, but only Ae A Ae, in principle, can be directly measured in e+e e+e but such process also receives a contribution rom the t channel diagram, which dilute the asymmetry 1

13 Experiments at the Z peak with unpolarized beams: the polarization I the polarization o the outgoing ermion can be measured (e.g. the lepton polarization can be determined rom its decay products), one can deine and measure the ollowing asymmetry (or average polarization): (NL/R number o outgoing let/right handed ) A pol L B NL NR N N L R TOT A can be directly measured too A In this case, we can also deine a Forward Backward polarization asymmetry, by separating let/right outgoing ermions in the orward or backward regions: A pol L R F L R B N L N R F N L N R B N N N N L R F L R B TOT Ae When we are able to determine the polarization o outgoing ermions (e.g. ), we have a direct estimation Ae too 13

14 Experiments with polarized beams: the Let Right asymmetry Let's assume we can choose the polarization o e beam (SLC case). Then we can measure: NL number o Z produced with let polarized e NR number o Z produced with right polarized e The ollowing Let Right asymmetry can be measured: ALR N L N R LR Ae N L N R TOT Direct measurement o Ae all Z decays (but e+e!) can be used detector acceptance and eiciencies are identical or let and right ermions beams must be highly polarized polarization must be measured ALR little statistical error little systematic error < Pe > mean polarization 1 N L N R Ae Pe N L N R CORRECTION 14

15 Experiments with polarized beams: the combined F B / L R asymmetry We deine the combined Let Right/Forward Backward asymmetry: NL / R F / B number o Forward / Backward events produced with Let / Right polarized e 4 N LF N LB N RF N RB 4 LR F LR B A 3 P e N LF N LB N RF N RB 3 TOT A FBLR With polarized beams, all the A can be directly measured! Thereore: with polarized beams (SLC) the asymmetries o all the identiiable ermions (e,,, c, b) can be directly measured with unpolarized beams (LEP) only Ae and A and the products Ae A can be directly measured 15

16 SLC: A0LR measurement Needed to evaluate the electron asymmetry Ae Hadronic decays o Z are used: e+e qq more statistics than leptonic decays need to reject e+e and inal states remaining background: 0.04% selection eiciency: ~ 91% (little amount o + not considered as a background) Measured Let Right asymmetry: Am (NL NR) / (NL + NR) Main corrections and systematics to be considered electron polarization: measured by Compton scattering o the e beam with a circularly polarized laser beam, using a Cerenkov spectrometer <Pe> background and machine related asymmetries Am ~ O(10 4) C.M. energy: needed to bring ALR to the Z pole value A0LR, eliminating the Z intererence and ISR contributions: a Z pole scan is perormed with o peak points AEW ~ % (remaining systematic error ~ 0.39%) Final result: 0 A LR (most precise determination rom a single measurement) 1 A A m AEW ± Pe m sin e ± (syst ) 16

17 SLC: Aℓ measurement Three independent measurements o Ae, A, A, using AFBLR Assuming the leptonic universality, the three results can be combined to evaluate one single Aℓ Same systematics o ALR measurement background estimation uncertainty negligible or ee, ( < ) shit o ± on A Results: Ae ± A 0.14 ± A ± Assuming lepton universality: A ℓ ± cos sin e ±

18 LEP: AFB0,ℓ measurement (I) Measured or all the lepton lavours Four independent measurements o each AFB Systematics rom selection and are small Detector related systematics (acceptance, charge assignment, etc.) are uncorrelated among the our experiments Common systematics mainly arise rom limits in theoretical precision and MC's Combined results o the our experiments: 0,e A FB ± , A FB ± , A FB ± , ℓ A FB ±

19 LEP: AFB0,ℓ measurement (II) 19

20 LEP: Aℓ measurement Exploiting the polarization o the outgoing lepton, both the A and Ae asymmetries can be measured (but not A!) Decay independent systematics are usually small and uncorrelated Decay dependent (related to the decay mode) systemtics are common to all experiments and must be taken into account in combination o the results Assuming e universality: 0 Aℓ ± sin e ±

21 LEP: AFB0,b measurement Use o b tagging algorithms independent measurements with leptonic and hadronic inal states can be combined 0,b A FB ±

22 AFB0, vs C.M. energy

23 SLC + LEP: determination o e Asymmetries sin e The two best estimations o sin e dier by more than 3! (reason still unknown!) 3

24 SLC + LEP: constraints on the SM mh ~ 100 GeV/c rom mean value, but mh ~ 30 GeV/c rom SLC Aℓ mh ~ 500 GeV/c rom LEP AFB0,b 4

25 Conclusions Described the concept o asymmetry and its importance Described the main asymmetry variables and how they can be measured Presented some results rom the main experiments (SLC LEP) Shown constraints on SM parameters rom asymmetries Reerences F. Hazeln, A.D. Martin, QUARKS AND LEPTONS: An Introductory Course in Modern Particle Physics, John Wiley & Sons The SLD Collaboration, Direct Measurement o Leptonic Coupling Asymmetries with Polarized Z s, arxiv:hep ex/970401v1 4 Apr 1997 The ALEPH, DELPHI, L3, OPAL, SLD Collaborations, Precision Electroweak Measurements on the Z Resonance, Physics Report Vol 47, pp , May 006 C. Mariotti, notes rom the course Fisica delle Particelle II or the Master Degree in Fisica delle Interazioni Fondamentali, University o Torino 5